From a well-known result [1]}, under Assumption REF  one has for any \(\rho \ge 0\)  and \(i=1,\ldots ,p\)  that
\(\Pr \left[\frac{1}{K}\sum _{k=0}^{K-1}g_i(x^k)-\frac{1}{K}\sum _{k=0}^{K-1}G_i(x^k,\xi _k)\ge \frac{\rho \sigma _c}{\sqrt{K}}\right]\le \exp \lbrace -\rho ^2/3\rbrace .\) 
